Chuck Schumer, the top Democrat in the Senate, in front of the Supreme Court on Tuesday. He said Democrats would use confirmation hearings to drill down on Judge Brett M. Kavanaugh’s views on executive power.CreditCreditErin Schaff for The New York Times

WASHINGTON — Senate Democrats, facing an uphill struggle to defeat the nomination of Judge Brett M. Kavanaugh to the Supreme Court, opened a broad attack on Tuesday, painting him as an archconservative who would roll back abortion rights, undo health care protections, ease gun restrictions and protect President Trump against the threat of indictment.

But as Judge Kavanaugh arrived at the Capitol to begin making courtesy calls on the senators who will decide his fate, the White House expressed confidence in the man that Mr. Trump introduced to the country as “one of the finest and sharpest legal minds of our time.”

The White House is embarking on an intensive sales campaign that has already enlisted more than 1,000 interest groups, including farmers and religious organizations, to build support for Judge Kavanaugh. Administration officials are pushing for hearings and a confirmation vote by Oct. 1, in time for the court’s new term.

In a sign of how difficult the Democrats’ path will be, Senator Susan Collins of Maine, a key swing vote, spoke favorably of Judge Kavanaugh on Tuesday, telling reporters, “When you look at the credentials that Judge Kavanaugh brings to the job, it’ll be very difficult for anyone to argue that he’s not qualified for the job.”

Washington is no stranger to bitter and divisive judicial confirmation fights, but the coming battle over Judge Kavanaugh is likely to be intense — and expensive. At a time when the United States is deeply polarized, with the ideological balance of the court at stake, Democrats and Republicans are keenly aware that Judge Kavanaugh, if confirmed, would push the court to the right, cementing its conservative majority and shaping American jurisprudence for decades to come.

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Judge Brett Kavanaugh met with Senator Charles E. Grassley, Republican of Iowa and the Senate Judiciary Committee chairman, on Tuesday on Capitol Hill.CreditLawrence Jackson for The New York Times

That has galvanized liberal and conservative advocacy groups, who began mobilizing even before the nomination was announced and expect to spend tens of millions through the summer and into the fall.

Judicial Crisis Network, a conservative advocacy group, has already posted a website — ConfirmKavanaugh.com — and is airing television ads. Leading social conservative political groups are rallying the anti-abortion grass-roots to support his confirmation with ads, rallies and online campaigns. Demand Justice, a liberal group, is running advertisements in Maine, aimed at Ms. Collins, as well in Alaska, the home state of another swing-vote Republican, Senator Lisa Murkowski.

But the positive comments from Ms. Collins — who voted in favor of Justices Elena Kagan and Sonia Sotomayor, two of President Barack Obama’s nominees — may have already shifted the pressure from leery Republicans to skittish Democrats running for re-election in states won handily by Mr. Trump in 2016.

Three of those Democrats — Senators Heidi Heitkamp of North Dakota, Joe Donnelly of Indiana and Joe Manchin III of West Virginia — voted to confirm Neil M. Gorsuch, nominated by Mr. Trump last year. None gave any hint on Tuesday of how they would vote on Judge Kavanaugh, but all will undoubtedly face intense pressure at home.

“I thought he came across as a good family person, good, decent human being,” Mr. Manchin said of his initial reaction to Judge Kavanaugh. But he said he would not be making a hasty decision about a Supreme Court appointment mere hours after the announcement, noting his concern about Judge Kavanaugh’s views of the Affordable Care Act given the “lives at stake” in West Virginia.

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The confirmation fight over President Trump’s Supreme Court nominee is underway. Here is what Judge Kavanaugh has said about the justices he admires, Roe v. Wade and the presidency.Published OnJuly 10, 2018CreditCreditT.J. Kirkpatrick for The New York Times

“You’ve got red-state Democrats who are up for re-election this year who are going to be faced with some pretty significant challenges with this vote,” said Senator Cory Gardner of Colorado, the chairman of the committee charged with electing Republicans to the Senate. “I think it’s a hot potato.”

In picking Judge Kavanaugh to fill the seat vacated by the retiring Justice Anthony M. Kennedy, Mr. Trump has turned to an experienced jurist with an Ivy League pedigree (Yale undergraduate and Yale Law), a deep conservative bent and a past in politics. Judge Kavanaugh worked under Kenneth W. Starr, the independent counsel who investigated President Bill Clinton; served in the administration of President George W. Bush; and joined the United States Court of Appeals for the District of Columbia Circuit in 2006.

Administration officials are betting that Judge Kavanaugh’s record of around 300 court decisions, combined with his ability to speak fluently on a range of complex issues, will make it impossible for Democrats to cast him as unqualified for Justice Kennedy’s seat. His effusive praise on Monday night of his mother and wife — and his coaching of his daughter’s basketball team — seemed aimed at defusing Democratic efforts to make him appear anti-woman.

“Judge Kavanaugh has impeccable credentials and interprets the law as it was written and intended,” said Raj Shah, a White House spokesman. “His record sells itself.”

Senator Joe Manchin III of West Virginia discussing the Supreme Court nominee at the Capitol on Tuesday. He is among a handful of Democratic senators from states that President Trump won handily who will face difficult decisions about whether to support the nominee.CreditLawrence Jackson for The New York Times

Among them: a 2017 case, Garza v. Hargan, where Judge Kavanaugh delayed an abortion for a 17-year-old immigrant who was in the United States illegally; a 2015 case, Priests for Life v. U.S. Department of Health and Human Services, where Judge Kavanaugh said the Affordable Care Act’s requirement for contraceptive coverage violated the religious freedom of religious nonprofits; and a 2011 dissent in Heller v. District of Columbia, where he argued the Second Amendment included the right to own a semiautomatic rifle.

Senator Chuck Schumer of New York, the Democratic leader, joined all of the Democrats on the Senate Judiciary Committee outside the Supreme Court on Tuesday to deliver a direct appeal to Americans to rise up in opposition to Judge Kavanaugh’s nomination. One by one, they ticked off warnings.

“If you are a young woman in America or you care about a young woman in America, pay attention to this,” said Senator Kamala Harris, Democrat of California. “Because it will forever change your life.”

Senator Richard Blumenthal, Democrat of Connecticut, issued a specific plea to the survivors of the school shooting in Parkland, Fla.: “If you care about common-sense gun violence protection, Judge Kavanaugh is your worst nightmare.”

Republicans, in turn, excoriated Democrats for not giving Mr. Trump’s nominee a chance.

“We’re less than 24 hours into this, and folks are already declaring that if you can’t see that Brett Kavanaugh is a cross between Lex Luthor and Darth Vader, then you apparently aren’t paying enough attention,” said Senator Ben Sasse, Republican of Nebraska. “The American people are smarter than that.”

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Senator Mitch McConnell, Republican of Kentucky and the majority leader, argued that it would be improper if Democrats tried to force the judge to say how he would decide issues in hypothetical cases.CreditLawrence Jackson for The New York Times

Senator Mitch McConnell, Republican of Kentucky and the majority leader, complained that Democrats had declared their opposition to Judge Kavanaugh even before his nomination was announced.

“They wrote statements of opposition only to fill in the name later,” the ordinarily staid Mr. McConnell said, growing exercised as he delivered his customary morning remarks on the Senate floor. “Senate Democrats were on record opposing him before he’d even been named! Just fill in the name! Whoever it is, we’re against.”

But Democrats were quick to call Mr. McConnell hypocritical, noting that when Mr. Obama nominated Judge Merrick B. Garland — a colleague of Judge Kavanaugh’s on the federal appeals court in Washington — many Republicans refused even to meet with Judge Garland, and denied him the opportunity to have a hearing.

Before Judge Kavanaugh’s nomination on Monday night, Democrats had centered their strategy on abortion rights and health care, warning that anyone Mr. Trump picked would overturn Roe v. Wade, the 1973 landmark decision legalizing abortion, and would imperil protections for people with pre-existing conditions under the Affordable Care Act.

But Judge Kavanaugh has given them a new line of attack: his past writings on the powers of the presidency, which go to the heart of the special counsel’s investigation of Mr. Trump. In 1998, Judge Kavanaugh wrote a law review article that raised doubts about whether a sitting president could be indicted. In another article, he argued that a sitting president should not be distracted by civil suits or criminal proceedings.

Democrats said Tuesday that those views would be a central focus of questioning during Mr. Kavanaugh’s confirmation hearings; already, some Democrats were calling for Judge Kavanaugh to pledge that he would recuse himself from any Supreme Court proceedings involving the president.

“We knew with any of the 25 nominees that health care and women’s health, right to choose would be important,” Mr. Schumer said, referring to the list of potential candidates drawn up for Mr. Trump by conservative groups during the 2016 campaign. “But Kavanaugh brings a new prominence to the issue of executive power because he is almost certainly the most hard right of all of the 25. He is almost certainly the one who would most yield to presidential power.”

A version of this article appears in print on , on Page A1 of the New York edition with the headline: Fierce and Costly Fight Over Court Nomination Commences in Capitol. Order Reprints | Today’s Paper | Subscribe